# 51 Blood pressure

Learning Objectives

After studying this section, you should be able to-

• Define blood flow, blood pressure, and peripheral resistance.
• State and interpret the equation that relates fluid flow to pressure and resistance.
• Describe the role of arterioles in regulating tissue blood flow and systemic arterial blood pressure.
• List the local, hormonal and neural factors that affect peripheral resistance and explain the importance of each.
• State the equation relating mean arterial pressure (MAP) to cardiac output (CO) and total peripheral resistance (TPR)
• Predict and describe how mean arterial pressure (MAP) would be affected by changes in total peripheral resistance (TPR) or by changes in cardiac output (CO) or any of its components – heart rate (HR), stroke volume (SV) or preload
• Given values for systolic and diastolic blood pressure, calculate pulse pressure (PP) and mean arterial pressure (MAP)

Blood flow refers to the movement of blood through a vessel, tissue, or organ, and is usually expressed in terms of volume of blood per unit of time. It is initiated by the contraction of the ventricles of the heart. If we consider the entire cardiovascular system, blood flow equals cardiac output. Ventricular contraction ejects blood into the major arteries, resulting in flow from regions of higher pressure to regions of lower pressure. This section discusses a number of critical variables that contribute to blood flow throughout the body. It also discusses resistance which is due to factors that impede or slow blood flow. Blood pressure is the force exerted by blood upon the walls of the blood vessels or the chambers of the heart. Blood pressure may be measured in both the systemic and pulmonary circulation.

# Arterial Blood Pressure

Arterial blood pressure in the larger vessels varies between systolic and diastolic pressures. Pulse pressure and mean arterial pressure are values that can be calculated based upon the systolic and diastolic pressures.

## Pulse Pressure

The difference between the systolic pressure and the diastolic pressure is the pulse pressure. For example, an individual with a systolic blood pressure (BP) of 120 mm Hg and a diastolic BP of 80 mm Hg would have a pulse pressure of 40 mmHg.

Pulse pressure = systolic BP – diastolic BP = 120 mmHg – 80 mmHg = 40 mmHg

Generally, a pulse pressure should be at least 25 percent of the systolic pressure. A pulse pressure below this level is described as low or narrow. This may occur, for example, in patients with a low stroke volume, which may be seen in congestive heart failure, stenosis of the aortic valve, or significant blood loss following trauma. In contrast, a high or wide pulse pressure is common in healthy people following strenuous exercise, when their resting pulse pressure of 30–40 mmHg may increase temporarily to 100 mmHg as stroke volume increases. A persistently high pulse pressure at or above 100 mmHg may indicate excessive resistance in the arteries and can be caused by a variety of disorders such as atherosclerosis. Chronic high resting pulse pressures can degrade the heart, brain, and kidneys, and warrant medical treatment.

## Mean Arterial Pressure

Mean arterial pressure (MAP) represents the “average” pressure of blood in the arteries, that is, the average force driving blood into vessels that serve the tissues. Mean is a statistical concept and is calculated by taking the sum of the values divided by the number of values. The mathematical formula for MAP divides the pulse pressure by three rather than two because the heart spends more time in diastole than it does in systole. MAP is not simply midway between systolic BP and diastolic BP, rather it is closer to diastolic BP. Although complicated to measure directly and complicated to calculate, MAP can be approximated by adding the diastolic pressure to one-third of the pulse pressure or systolic pressure minus the diastolic pressure:

MAP = ⅔ diastolic BP + ⅓ systolic BP

This weighted average accounts for the fact that the heart is in diastole for ⅔ of the time and systole for ⅓ of the time. Normally, the MAP falls within the range of 70–110 mm Hg. If the value falls below 60 mm Hg for an extended time, blood pressure will not be high enough to ensure circulation to and through the tissues, which results in ischemia, or insufficient blood flow. A condition called hypoxia, inadequate oxygenation of tissues, commonly accompanies ischemia. The term hypoxemia refers to low levels of oxygen in systemic arterial blood. Neurons are especially sensitive to hypoxia and may die or be damaged if blood flow and oxygen supplies are not quickly restored.

# Variables Affecting Blood Flow and Blood Pressure

Four variables influence blood flow and blood pressure: cardiac output which has been discussed previously, resistance (to be discussed below), and compliance and blood volume (discussed in future sections).

Recall that blood moves from higher pressure to lower pressure. It is pumped from the heart into the arteries at high pressure. Since pressure in the veins is normally relatively low, for blood to flow back into the heart, the pressure in the atria during atrial diastole must be even lower. It normally approaches zero, except when the atria contract.

Resistance

The three most important factors affecting resistance are blood viscosity, vessel length and vessel diameter and are each considered below.

Blood viscosity is the thickness of fluids and how it affects fluid flow. Clean water, for example, is less viscous than mud and flows more easily than mud. The viscosity of blood is directly proportional to resistance and inversely proportional to flow; therefore, any condition that causes viscosity to increase will also increased resistance and decreased flow. For example, imagine sipping milk, then a milkshake, through the same size straw. You experience more resistance and therefore less flow from the milkshake compared to the milk. Conversely, any condition that causes viscosity to decrease (such as when the milkshake melts) will decrease resistance and increase flow.

Normally the viscosity of blood does not change over short periods of time. The two primary determinants of blood viscosity are the formed elements and plasma proteins. Since most formed elements are erythrocytes, any condition affecting erythropoiesis, such as polycythemia or anemia, can alter viscosity. Since most plasma proteins are produced by the liver, any condition affecting liver function can also change the viscosity slightly and therefore decrease blood flow. Liver abnormalities include hepatitis, cirrhosis, alcohol damage, and drug toxicities. While leukocytes and platelets are normally a small component of the formed elements, there are some rare conditions in which severe overproduction can impact viscosity as well.

Blood vessel length is directly proportional to resistance: the longer the vessel, the greater the resistance and the lower the flow. As with blood volume, this makes intuitive sense since the increased surface area of the vessel wall will impede the flow of blood. There is friction between the flowing blood and vessel wall. Likewise, if the vessel is shortened, the resistance will decrease, and flow will increase.

The length of our blood vessels increases throughout childhood as we grow, of course, but is unchanging in adults under normal physiological circumstances. Further, the distribution of vessels is not the same in all tissues. Adipose tissue does not have an extensive vascular supply. One pound of adipose tissue contains approximately 200 miles of vessels, whereas skeletal muscle contains more than twice that. Overall, vessels decrease in length only during loss of mass or amputation. An individual weighing 150 pounds has approximately 60,000 miles of vessels in the body. Gaining about 10 pounds adds from 2000 to 4000 miles of vessels, depending upon the nature of the gained tissue (e.g., muscle or fat). One of the great benefits of weight reduction is the reduced stress to the heart, which does not have to overcome the resistance of as many miles of vessels.

In contrast to length, the blood vessel diameter changes throughout the body, according to the type of vessel, as we discussed earlier. The diameter of any given vessel may also change frequently throughout the day in response to neural and chemical signals that trigger vasodilation and vasoconstriction. The vascular tone of the vessel is the contractile state of the smooth muscle and the primary determinant of diameter, and thus of resistance and flow. The effect of vessel diameter on resistance is inverse: Given the same volume of blood, an increased diameter means there is less blood contacting the vessel wall, thus there is less friction and less resistance, subsequently increasing flow. A decreased diameter means more of the blood contacts the vessel wall, and resistance increases, subsequently decreasing flow.

The influence of lumen diameter on resistance is dramatic: A slight increase or decrease in diameter causes a dramatic decrease or increase in resistance. This is because resistance is inversely proportional to the radius of the blood vessel (one-half of the vessel’s diameter) raised to the fourth power (R = 1/r4). This means, for example, that if an artery or arteriole constricts to one-half of its original radius, the resistance to flow will increase 16 times. And if an artery or arteriole dilates to twice its initial radius, then resistance in the vessel will decrease to 1/16 of its original value and flow will increase 16 times.

A Mathematical Approach to Factors Affecting Blood Flow

Jean Louis Marie Poiseuille was a French physician and physiologist who devised a mathematical equation describing blood flow and its relationship to known parameters. Although understanding the math behind the relationships among the factors affecting blood flow is not necessary to understand blood flow, it can help solidify an understanding of their relationships. There are three critical variables: radius (r), vessel length (λ), and viscosity (η).

Poiseuille’s equation:

Blood flow = ΔP x (πr4/8ηλ)

• ΔP represents the difference in pressure.
• π = pi
• r4 is the radius (one-half of the diameter) of the vessel to the fourth power.
• η is the Greek letter eta and represents the viscosity of the blood.
• λ is the Greek letter lambda and represents the length of a blood vessel.

One of several things this equation allows us to do is calculate the resistance in the vascular system. Normally this value is extremely difficult to measure, but it can be calculated from this known relationship:

Blood flow = ΔP/Resistance

If we rearrange this slightly,

Resistance = ΔP/Blood flow

Then by substituting Pouseille’s equation for blood flow:

Resistance =8ηλ/πr4

By examining this equation, you can see that there are only three variables: viscosity, vessel length, and radius, since 8 and π are both constants. The important thing to remember is this: Two of these variables, viscosity and vessel length, will change slowly in the body. Only one of these factors, the radius, can be changed rapidly by vasoconstriction and vasodilation, thus dramatically impacting resistance and flow. Further, small changes in the radius will greatly affect flow, since it is raised to the fourth power in the equation.

We have briefly considered how cardiac output and blood volume impact blood flow and pressure; the next step is to see how the other variables (contraction, vessel length, and viscosity) articulate with Pouseille’s equation and what they can teach us about the impact on blood flow.

Adapted from Anatomy & Physiology by Lindsay M. Biga et al, shared under a Creative Commons Attribution-ShareAlike 4.0 International License, chapter 20

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